Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Sabah Benadouane; Aziza Berbache; Ahmed Bendjeddou

doi:10.2478/tmmp-2021-0018

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Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Tatra Mountains Mathematical Publications

Volume 79 (2021): Issue 2 (December 2021)

By: Sabah Benadouane, Aziza Berbache and Ahmed Bendjeddou

Open Access

|Jan 2022

Abstract

The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6k + 1, k ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0018 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 33 - 46

Submitted on: Nov 13, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Algebraic and non–algebraic limit cycle,

planar polynomial differential system,

first integral

Related subjects:

Mathematics,

General mathematics

© 2022 Sabah Benadouane, Aziza Berbache, Ahmed Bendjeddou, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 79 (2021): Issue 2 (December 2021)